(t)=10t-5t2

Solution for (t)=10t-5t2 equation:

(t)=10t-5t^2

We move all terms to the left:

(t)-(10t-5t^2)=0

We get rid of parentheses

5t^2-10t+t=0

We add all the numbers together, and all the variables

5t^2-9t=0

a = 5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·5·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*5}=\frac{18}{10}
=1+4/5
$